I try to both categorize all of the songs I have, but not get caught up in the whole naming game. My goal is to simply group music by songs that sound good together. Then, if I really wanted to completely mix styles, it would be my choice not the default. I tend to listen to styles/genres/subgenres/etc. based on whatever mood I happen to be in and I have a LOT of different things to choose from! In many cases, without shuffle-playing a subsection of my music, I have found that I would have completely missed out on stuff that's really good but obscure. Quite often I'll have to look to see what's playing when I hear something I'm not familiar with that sounds good.
So, when I refer to something as "Prog," it typically means music that is labelled as such in general by most people. I don't get into the debates and arguments about whether a certain artist is "Progressive" or not (heck, Beethoven could be argued to have been progressive at his time!).
Most people with smaller song collections also tend to stick with a relatively small area of music that they prefer. I have at least 250,000 songs that are all over the place: Classical, New Wave, New Age, Progressive, Rock (in many, many forms), Metal (also in many forms), Electonic (Trance, Techno, Ambient, House, etc., etc., etc.), Psychedelic, Punk, Ska, Reggae, Latin, Celtic, Dance, Pop, Soul, Funk, Folk, World, R&B, Industrial and lots of kinds of Jazz. Heck, I even have too much inherited music like Easy Listening and Big Band. My hard drive with the media player is currently down so I can't check these, but I'm sure I've even missed one or two.
Some of those subgenres I'm rarely in the mood for, others I can listen to every day. I really don't want them all mixed together!